 
Summary: Matrix Compression using the Nystr¨om Method
Arik Nemtsov1
Amir Averbuch1
Alon Schclar2
1
School of Computer Science
Tel Aviv University, Tel Aviv 69978
2
School of Computer Science
The Academic College of Tel AvivYaffo ,Tel Aviv, 61083
Abstract
The Nystr¨om method is routinely used for outofsample extension of kernel ma
trices. We describe how this method can be applied to find the singular value de
composition (SVD) of general matrices and the eigenvalue decomposition (EVD) of
square matrices. We take as an input a matrix M Rm×n, a user defined integer
s min(m, n) and AM Rs×s, a matrix sampled from columns and rows of M. These
are used to construct an approximate ranks SVD of M in O s2 (m + n) operations.
If M is square, the ranks EVD can be similarly constructed in O s2n operations. In
this sense, AM is a compressed version of M.
We discuss theoretical considerations for the choice of AM and how it relates to the
